Solve the System of Inequalities 4x-39>-43 ; AND , 8x+31<23

$4 x - 39 > - 43$ ; AND , $8 x + 31 < 23$

Step 1

Solve $4 x - 39 > - 43$ for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Add $39$ to both sides of the inequality.

$4 x > - 43 + 39$

Add $- 43$ and $39$ .

$4 x > - 4$

Divide each term in $4 x > - 4$ by $4$ and simplify.

Divide each term in $4 x > - 4$ by $4$ .

$\frac{4 x}{4} > \frac{- 4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{- 4}{4}$

Divide $x$ by $1$ .

$x > \frac{- 4}{4}$

Simplify the right side.

Divide $- 4$ by $4$ .

$x > - 1$

Step 2

Solve $8 x + 31 < 23$ for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Subtract $31$ from both sides of the inequality.

$8 x < 23 - 31$

Subtract $31$ from $23$ .

$8 x < - 8$

Divide each term in $8 x < - 8$ by $8$ and simplify.

Divide each term in $8 x < - 8$ by $8$ .

$\frac{8 x}{8} < \frac{- 8}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} < \frac{- 8}{8}$

Divide $x$ by $1$ .

$x < \frac{- 8}{8}$

Simplify the right side.

Divide $- 8$ by $8$ .

$x < - 1$

Step 3

Find the intersection of $x > - 1$ and $x < - 1$ .

No solution